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2 Answers
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Among the handwriting styles 章草, 今草 and 狂草, 今草 is the most frequently used. However, compared with 今草, 行书 is even more popular.

That's because:

章草 is the rapid writing of 隶书. Currently, Chinese teachers don't teach 隶书 in primary schools for its old style. Only calligraphy amateurs and experts would learn 隶书 so as 章草.

今草 is based on 楷书 -- 楷书 is formally taught in primary schools -- but 今草 is seldom used by young people, as it's hard to recognize. (Well, I mean the rigorous 今草, but not squiggles at random.) 狂草 is an even faster handwriting of 今草, now I can just see that in calligraphy art works, doctors' prescriptions, and some old educated persons' handwritings.

行书(行楷) takes both the identifiability and the efficiency into account, so it's the most popular.

I don't know whether there's any statistical research work about the most frequently used handwriting style. Now less and less people need to write something by hand, as computers and the internet are occupying our life :( So a person with good handwriting is less seen now.

The most frequently used Chinese computer font should be 宋体, most characters in newspapers and official documents and books are printed in 宋体.

If you want to learn something about the most frequently used handwriting. You can search 行书字帖 in Google, and then you can find many. Because I am not sure about whether they are infringement of copyright, I don't leave any links here :)

By the way, I don't recommend using the computer font 华文行楷 as the handwriting model for practice. Because it's just designed for printing -- and personally, one of my friends, a professional graphic artist, says that font is making people feel visual fatigue.

EDIT

In fact, 章草 consists of seven types:

原始型, 简章型, 标准型, 章今型, 今章型, 正章型, and 章篆型

The most typical 章草 is 标准型 (standard type, the name has suggested that). 急就章 by Song Ke in Ming Dynasty is one master work of 章草:

As you can find in some characters, some 隶书's styles -- like 燕尾 (swallow's tail) -- still persist. (Note: according to some references, the first character on the top-right is controversial. In the resource providing by Taiwan National Palace Museum, it's 賣; According to 急就篇, it is said to be 洞 or 𨽍. In this picture, it should be 𨽍.)

Master work of 今草: 冠军帖 by Zhang Zhi, in Han Dynasty. It's more fluent than 章草.

Master work of 狂草: 古诗四帖 by Zhang Xu, in Tang Dynasty.
Which says

东明九芝盖，北烛五云车。飘飖入倒景，出没上烟霞。春泉下玉溜，青鸟向金华。汉帝看桃核，齐侯问棘花。应逐上元酒，同来访蔡家。

狂草 is the most casual-like works, and written at an as-fast-as-possible speed. Notice that, casual-like is not casual, it doesn't mean you can freely write something very fast and then call it 狂草 (though, we sometimes make fun to call that kind of handwriting "狂草", with quotation marks). In fact, one needs to learn much about 楷书, experience the laws and spirit of Chinese calligraphy, and then they can write good 狂草 works with a rigorous but casual attitude. It's not easy.

Master work of 行书: 兰亭集序 by Wang Xizhi, in Eastern Jin Dynasty.
This is the most famous Chinese calligraphy works ever. (Yes, I didn't say one of the most.) High school students in China are required to recite the paragraphs of 兰亭集序. This is also considered as a paragon for 行书 learners.

@Manjusri: You're welcome. If you have any questions about the answer, please feel free to leave them in the comment.
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StanJun 8 '13 at 7:18

In response to 谢谢, Chinese always say 不(用)谢 or 不客气 or （你）（太）客气了. Today, the young people in China, they prefer to use '3q' sound like 'thank you' or '3ks' sound like 'Thanks' to express their appreciation on web.
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Eden HarderAug 13 '13 at 2:13

The most used style in life is 楷体. The suggested way to learn how to write in each style is imitate a copybook for calligraphy with a good pen. I recommend the ones written by 庞中华. You can buy from amazon http://www.amazon.cn/s?ie=UTF8&page=1&rh=n%3A658390051%2Ck%3A%E5%BA%9E%E4%B8%AD%E5%8D%8E%E5%AD%97%E5%B8%96 or you write all the characters in a document in the style you like and then print it as a copybook for calligraphy. If you need the 庞中华 style of 楷体, leave your email and I will send it to you, since I do not know one can download it outside China.

草书 only appears in some artistic works, and even most Chinese can not recognize the characters in the style of 草书. What's more, 狂草 even the author cannot recognize the words he wrote down sometimes. In comparison, 行书 is more general. The most used style in life is 楷体. BTW, there is 行楷 between 楷体 and 行书. You'd better learn in this order 楷体 行楷 行书 草书. It requires great effort and a long time. But it is very comfortable if you can write in these styles.